Thanks to all who chipped in with advice for me on this point.
My connection in Doha had me landing about 6:00 p.m. After a surprisingly painless bus ride and a quick security screening I made my way into the biggest duty free shopping area I have *EVER* seen. The cornucopia of luxury goods, I expected. But giant sacks of American candy? Who needs 250 Twix bars?
But I digress. The wait to purchase access to the Oryx Lounge took about 90 seconds and the guy who ran my credit card was cheerful and efficient. The lounge itself was nothing special, but it sure beat the terminal. I liked the chopped tomato salad, the olives and the various pastries. Didn't sample the adult beverages. Not crowded at all. There were even a couple of free recliners in the darkened sleeping area. Wi-fi was spotty in some locations, but moving to a different spot cured that.
Wanted to take a shower and wandered around for some time before I discovered you have to ask one of the attendants for a towel. The showers (which are next to the toilets) were huge compared to some other lounges I've been to, with plenty of hot water and good water pressure. The ventilation was good enough that even after I took a serious shower the steam cleared quickly and my clothes weren't too damp.
At a price of $40 U.S. dollars for (I think) up to three hours, I think the Oryx Lounge is a decent value.